(英汉双语)流体力学第三章流体动力学基础.ppt
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1、1,Chapter 3Basis of Fluid Dynamics,Fluid Mechanics,2,第三章 流体动力学基础,3,Chapter 3 Basis of Fluid Dynamics,34 Continuity Equation,31 Preface,32 Methods to Describe Fluid Motion,33 Basic Concepts of Fluid Motion,35 Motion Differential Equation of Ideal Fluid,36 Bernoulli Equation and Its Application,37 Sys
2、tem and Control Volume,38 Momentum Equation,39 Moment of Momentum Equation Exercises of Chapter 3,4,第三章 流体动力学基础,34 连续方程式,31 引言,32 描述流体运动的方法,33 流体运动的基本概念,35 理想流体的运动微分方程,36 伯努利方程及其应用,37 系统与控制体,38 动量方程,39 动量矩方程 第三章 习 题,5,Chapter 3 Basis of Fluid Dynamics,3-1 Preface,Basis of Fluid Dynamics,The backgrou
3、nds,fundamentals and fundamental equations of fluid dynamics all have certain relations with each part of engineering fluid mechanics,so this chapter is the emphases in the whole lessons.,6,第三章 流体动力学基础,3-1 引言,流体动力学基础,流体动力学的基础知识,基本原理和基本方程与工程流体力学的各部分均有一定的关联,因而本章是整个课程的重点。,7,3-2 Methods to Describe the
4、Fluid Motion,Methods to describe the fluid motion:,1.Lagranges method,Definition:,Lagranges method is to consider the fluid particles as research objects and to research the motion course of each particle,and then gain the kinetic regulation of the whole fluid through synthesizing motion instances o
5、f all being researched objects.The essential of lagrangian method is a method of particle coordinates.,Basis of Fluid Dynamics,8,3-2 描述流体运动的方法,描述流体运动的方法:,一、拉格朗日法,定义:,把流体质点作为研究对象,研究各质点的运动历程,然后通过综合所有被研究流体质点的运动情况来获得整个流体运动的规律,这种方法叫做拉格朗日法。实质是一种质点系法。,流体动力学基础,9,when we use lagranges method to describe the
6、fluid motion the position coordinates of motion particles are not independent variables but functions of original coordinate a,b,c and time variable t,that is,(31),In this formula,a,b,c and t are all called lagrangian variables.Different particles have different original coordinates.,Difficulties wi
7、ll be met when using lagranges method to analyze fluid motion on math except for fewer instances(such as researching wave motion).Eulers method is used mostly in fluid motion.,Basis of Fluid Dynamics,10,用拉格朗日法描述流体的运动时,运动质点的位置坐标不是独立变量,而是起始坐标a、b、c和时间变量 t 的函数,即,(31),式中a,b,c,t 统称为拉格朗日变量,不同的运动质点,起始坐标不同。,
8、用拉格朗日法分析流体运动,在数学上将会遇到困难。除少数情况外(如研究波浪运动),在流体运动中多采用欧拉法。,流体动力学基础,11,2.Eulers method,Definition:,When we use Eulers method to describe fluid motion the motion factors are continuous differential functions of space coordinates x,y,z and time variable t.x,y,z and t are called Eulers variables.So the,veloc
9、ity field can be expressed by the following formulas:,(32),With a view to the space points in the fluid field(the space full of motion fluid)without researching the moving course of each particle.It is to synthesize enough space points to gain the regulation of the whole fluid by observing the regul
10、ations of motion factors of particle flowing via each space point changing with time which is called Eulers method(fluid field method).,Basis of Fluid Dynamics,12,二、欧拉法,定义:,用欧拉法描述流体的运动时,运动要素是空间坐标x,y,z和时间变量t的连续可微函数。x,y,z,t 称为欧拉变量,因此,速度场可表示为:,(32),不研究各个质点的运动过程,而着眼于流场(充满运动流体的空间)中的空间点,即通过观察质点流经每个空间点上的运动
11、要素随时间变化的规律,把足够多的空间点综合起来而得出整个流体运动的规律,这种方法叫做欧拉法(流场法)。,流体动力学基础,13,Pressure field and density field can be expressed as:,In the formula(32)x,y and z are motion coordinates of fluid particles at time t and namely are functions of time variable t.So according to the principle of compound function differen
12、tiate and also think over the following formulas:,The acceleration components in direction of space coordinates of x,y,z are:,(35),Basis of Fluid Dynamics,14,压强和密度场表示为:,式(32)中x,y,z是流体质点在 t 时刻的运动坐标,即是时间变量 t 的函数。因此,根据复合函数求导法则,并考虑到,可得加速度在空间坐标x,y,z方向的分量为,(35),流体动力学基础,15,The vector expression is,(35a),In
13、 it,When using Eulers method to query variance ratio of other motion factors of fluid particle changing with time the normal formula is,(36),is called total derivative,is called local derivative,is called migratory derivative.,Basis of Fluid Dynamics,16,矢量式为,(35a),其中,用欧拉法求流体质点其它运动要素对时间变化率的一般式子为,(36)
14、,称 为全导数,为当地导数,为迁移导数。,流体动力学基础,17,3-3 Basic Concepts of Fluid Motion,1.Stationary flow and nonstationary flow,Definition:,In factual engineering problems,motion factors of quite a few un steady flow changing with time very slowly which can be treated as steady flow problems approximatively.,Or else it
15、 is called nonstationary flow.,If all motion factors of each space point on fluid field dont change with time,this kind of flow is called steady flow.that is:,Basis of Fluid Dynamics,18,3-3 流体运动的基本概念,一、定常流动与非定常流动,定义:,在实际工程问题中,不少非定常流动问题的运动要素随时间变化非常缓慢,可近似地作为定常流动来处理。,否则,称为非定常流动。,若流场中各空间点上的一切运动要素都不随时间变化
16、,这种流动称为定常流动。即,流体动力学基础,19,2.Trace and Streamline,Definition:,Figure 31 Trace,According to the differential equation of trace line is,(37),When using Lagrange method to describe fluid motion the concept of trace line is introduced,(1).Trace,On special situation(x,y,z)the track of a certain fluid parti
17、cle moveing with time is shown in Figure 3-1.,Basis of Fluid Dynamics,20,二、迹线和流线,定义:,根据 迹线微分方程为,(37),流体动力学基础,用拉格朗日法描述流体运动引进迹线概念。,1、迹线,特定位置(x,y,z)处某流体质点随时间推移所走的轨 迹。如图31所示。,21,Basis of Fluid Dynamics,22,2、流线,定义:,流线的微分方程:,设流线上一点的速度矢量为流线上的微元线段矢量 根据流线定义,可得用矢量表示的微分方程为,(38),若写成投影形式,则为,(38a),流体动力学基础,用欧拉法形象地
18、对流场进行几何描述,引进了流线的概念。,某一瞬时在流场中绘出的曲线,在这条曲线上所有质点的速度矢量都和该曲线相切,则此曲线称为流线。如图32。,23,example 31 Given that the velocity filed is,In it,k is constant,try to query the streamline equation.,Basis of Fluid Dynamics,24,例题31已知速度场为,其中k为常数,试求流线方程。,由式(38a)有,积分上式的流线方程为,如图33所示,该流动的流线为一族等角双曲线。,流线的性质:,解根据 及 可知流体运动仅限于 的上半平
19、面。,流体动力学基础,(1)一般情况下,流线不能相交,且只能是一条光滑曲线;(2)在定常流动条件下,流线的形状、位置不随时间变化,且流线与迹线重合。,25,3.Stream tube,stream flow and cross section of flow,Definition:,(1).Stream tube,Take a random close curve C on fluid field,draw streamlines via every points on C,the pipe surrounded by these streamlines is called stream tu
20、be.As shown in Figure 34.,Because streamlines cant intersect fluid particles only can flow in the stream tube or via the surface of flow pipe on each time but cant go through the stream tube.so the stream tube just likes a really tube.,Basis of Fluid Dynamics,26,三、流管、流束与过流断面,定义:,由于流线不能相交,所以各个时刻,流体质点
21、只能在流管 内部或沿流管表面流动,而不能穿越流管,故流管仿佛就是一 根真实的管子。,流体动力学基础,1、流管,在流场中取任意封闭曲线C,经过曲线C的每一点作流线,由这些流线所围成的管称为流管。如图34所示。,27,Basis of Fluid Dynamics,28,2、流束,3、过流断面,当组成流束的所有流线互相平行时,过流断面是平面;否则,过流断面是曲面。,流体动力学基础,流管内所有流线的总和称为流束。断面无穷小的流束称为微小流束,(元流)如图35中断面为 的流束。无数微小流束的总和称为总流。,定义:,与流束中所有流线正交的横断面称为过流断面。如图36所示。,定义:,29,4.Discha
22、rge and average velocity of section,(1).Discharge,Definition:,The fluid quantity through a certain spatial curved surface in unit time is called Discharge.,In this formula is the cosine of inclination of velocity vector and the unit vector in normal orientation of infinitesimal area.,Basis of Fluid
23、Dynamics,30,四、流量与断面平均速度,1、流量,定义:,两种表示方法:,流经任意曲面的流量,(310),式中 为速度矢量与微元面积 法线方向单位矢量 的夹角余弦。,流体动力学基础,单位时间内通过某一特定空间曲面的流体量称为流量。,31,(2).Average velocity of section,5.One-,two-,and three dimensional flow,The discharge Q flowing across the cross section of flow is divided by area of cross section A.namely,defi
24、nition:,The motion factor which is the function of a coordinate is called one-dimensional flow.The motion factor which is the function of two coordinates is called two-dimensional flow.The motion factor which is the function of three coordinates is called three-dimensional flow.,definition:,Basis of
25、 Fluid Dynamics,32,2、断面平均流速,五、一元流动、二元流动、与三元流动,流体动力学基础,定义:,运动要素是一个坐标的函数,称为一元流动。运动要素是二个坐标的函数,称为二元流动。运动要素是三个坐标的函数,称为三元流动。,定义:,33,3-4 Continuity Equation,Take a infinitesimal hexahedron on a random point in fluid field.as shown in Figure 37。The mass of it changes with space and time.,(1)Space change,for
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